The multiscenario lot size problem with concave costs

The dynamic single-facility single-item lot size problem is addressed. The finite planning horizon is divided into several time periods. Although the total demand is assumed to be a fixed value, the distribution of this demand among the different periods is unknown. Therefore, for each period the demand can be chosen from a discrete set of values. For this reason, all the combinations of the demand vector yield a set of different scenarios. Moreover, we assume that the production/reorder and holding cost vectors can vary from one scenario to another. For each scenario, we consider as the objective function the sum of the production/reorder and the holding costs. The problem consists of determining all the Pareto-optimal or non-dominated production plans with respect to all scenarios. We propose a solution method based on a multiobjective branch and bound approach. Depending on whether shortages are considered or not, different upper bound sets are provided. Computational results on several randomly generated problems are reported

Modeling Industrial Lot Sizing Problems: A Review

In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems. The focus of this paper is on the modeling various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research

Tradeoff Analysis for Optimal Multiobjective Inventory Model

Deterministic inventory model, the economic order quantity (EOQ), reveals that carrying inventory or ordering frequency follows a relation of tradeoff. For probabilistic demand, the tradeoff surface among annual order, expected inventory and shortage are useful because they quantify what the firm must pay in terms of ordering workload and inventory investment to meet the customer service desired. Based on a triobjective inventory model, this paper employs the successive approximation to obtain efficient control policies outlining tradeoffs among conflicting objectives. The nondominated solutions obtained by successive approximation are further used to plot a 3D scatterplot for exploring the relationships between objectives. Visualization of the tradeoffs displayed by the scatterplots justifies the computation effort done in the experiment, although several iterations needed to reach a nondominated solution make the solution procedure lengthy and tedious. Information elicited from the inverse relationships may help managers make deliberate inventory decisions. For the future work, developing an efficient and effective solution procedure for tradeoff analysis in multiobjective inventory management seems imperative

Modeling and Optimization of Gas Networks in Refinery

Master'sMASTER OF ENGINEERIN

Bi-criteria network optimization: problems and algorithms

Several approaches, exact and heuristics, have been designed in order to generate the Pareto frontier for multi-objective combinatorial optimization problems. Although several classes of standard optimization models have been studied in their multi- objective version, there still exists a big gap between the solution techniques and the complexity of the mathematical models that derive from the most recent real world applications. In this thesis such aspect is highlighted with reference to a specific application field, the telecommunication sector, where several emerging optimization problems are characterized by a multi-objective nature. The study of some of these problems, analyzed and solved in the thesis, has been the starting point for an assessment of the state of the art in multicriteria optimization with particular focus on multi-objective integer linear programming. A general two-phase approach for bi-criteria integer network flow problems has been proposed and applied to the bi-objective integer minimum cost flow and the bi-objective minimum spanning tree problem. For both of them the two-phase approach has been designed and tested to generate a complete set of efficient solutions. This procedure, with appropriate changes according to the specific problem, could be applied on other bi-objective integer network flow problems. In this perspective, this work can be seen as a first attempt in the direction of closing the gap between the complex models associated with the most recent real world applications and the methodologies to deal with multi-objective programming. The thesis is structured in the following way: Chapter 1 reports some preliminary concepts on graph and networks and a short overview of the main network flow problems; in Chapter 2 some emerging optimization problems are described, mathematically formalized and solved, underling their multi-objective nature. Chapter 3 presents the state of the art on multicriteria optimization. Chapter 4 describes the general idea of the solution algorithm proposed in this work for bi-objective integer network flow problems. Chapter 5 is focused on the bi-objective integer minimum cost flow problem and on the adaptation of the procedure proposed in Chapter 4 on such a problem. Analogously, Chapter 6 describes the application of the same approach on the bi-objective minimum spanning tree problem. Summing up, the general scheme appears to adapt very well to both problems and can be easily implemented. For the bi-objective integer minimum cost flow problem, the numerical tests performed on a selection of test instances, taken from the literature, permit to verify that the algorithm finds a complete set of efficient solutions. For the bi-objective minimum spanning tree problem, we solved a numerical example using two alternative methods for the first phase, confirming the practicability of the approach

Understanding Complexity in Multiobjective Optimization

This report documents the program and outcomes of the Dagstuhl Seminar 15031 Understanding Complexity in Multiobjective Optimization. This seminar carried on the series of four previous Dagstuhl Seminars (04461, 06501, 09041 and 12041) that were focused on Multiobjective Optimization, and strengthening the links between the Evolutionary Multiobjective Optimization (EMO) and Multiple Criteria Decision Making (MCDM) communities. The purpose of the seminar was to bring together researchers from the two communities to take part in a wide-ranging discussion about the different sources and impacts of complexity in multiobjective optimization. The outcome was a clarified viewpoint of complexity in the various facets of multiobjective optimization, leading to several research initiatives with innovative approaches for coping with complexity